How many different committees can be formed from 12 teachers and 43 students if the committee consists of 3 teachers and 4 ​students? The committee of 7 members can be selected in BLANK
different ways.​

Step-by-step explanation:

we are two conditions

In choosing a committee, order doesn't matter; in case of teachers we need the number of combinations of 3 people chosen from 12

remember that,

with the condition we obtain that,

therefore substitute:

simplify Parentheses:

rewrite:

reduce fraction:

rewrite 12 and 10:

reduce fraction:

simplify multiplication:

In case of students we need the number of combinations of 4 students choosen from 43 therefore,

simplify which yields:

hence,

The committee of 7 members can be selected in BLANK different ways is

and we're done!

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.